najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2015-6-5-672-679najo-991Research ArticlePHYSICSФИЗИКАAnalytical benchmark solutions for nanotube flows with variable viscosityMakeevI. V.

49, Kronverkskiy, St. Petersburg, 197101

BlinovaI. V.

49, Kronverkskiy, St. Petersburg, 197101

PopovI. Yu.

49, Kronverkskiy, St. Petersburg, 197101

popov1955@gmail.comITMO UniversityRussian Federation20151508202565672679Copyright © Makeev I.V., Blinova I.V., Popov I.Y., 20252025Makeev I.V., Blinova I.V., Popov I.Y.Makeev I.V., Blinova I.V., Popov I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/991

Three-dimensional Stokes equations with variable viscosity in cylindrical coordinates are considered. This case is natural for flow through a nanotube in biological applications. We obtain exact particular solutions – a benchmark for numerical approache. 

Stokes flowvariable viscositymultigrid methodsbenchmark solutionsThis work was partially financially supported by the Government of the Russian Federation (grant 074-U01), by Ministry of Science and Education of the Russian Federation (GOSZADANIE 2014/190, Projects No 14.Z50.31.0031 and No. 1.754.2014/K)), by grant MK-5001.2015.1 of the President of the Russian Federation. The authors thank Prof. P. Tackley and Prof. T. Gerya for interesting discussions.ReferencesZhang H., Xu Sh., Jeffries G.D.M., Orwar O., Jesorka A. Artificial nanotube connections and transport of molecular cargo between mammalian cells. Nano Comm. Net., 2013, 4(4), P. 197–204.Zhang H., Xu Sh., Jeffries G.D.M., Orwar O., Jesorka A. Artificial nanotube connections and transport of molecular cargo between mammalian cells. Nano Comm. Net., 2013, 4(4), P. 197–204.Li T.-D., Gao J., Szoszkeiwicz R., Landman U., Riedo E. Structured and viscous water in subnanometr gaps. Phys. Rev. B, 2007, 75, P. 115415.Li T.-D., Gao J., Szoszkeiwicz R., Landman U., Riedo E. Structured and viscous water in subnanometr gaps. Phys. Rev. B, 2007, 75, P. 115415.Popov I.Yu., Chivilikhin S.A., Rodygina O.A., Gusarov V.V. Crystallite model for flow in nanotube caused by wall soliton. Nanosystems: Phys. Chem. Math., 2014, 5(3), P. 400–404.Popov I.Yu., Chivilikhin S.A., Rodygina O.A., Gusarov V.V. Crystallite model for flow in nanotube caused by wall soliton. Nanosystems: Phys. Chem. Math., 2014, 5(3), P. 400–404.Popov I. Statistical derivation of modified hydrodynamic equations for nanotube flows. Phys. Scripta, 2011, 83, P. 045601/1-5.Popov I. Statistical derivation of modified hydrodynamic equations for nanotube flows. Phys. Scripta, 2011, 83, P. 045601/1-5.Mashl R.J., Joseph S., Aluru N.R., Jacobsson E. Anomalously immobilized water: A new water phase induced by confinement in nanotubes. Nano Letters, 2003, 3(5), P. 589–592.Mashl R.J., Joseph S., Aluru N.R., Jacobsson E. Anomalously immobilized water: A new water phase induced by confinement in nanotubes. Nano Letters, 2003, 3(5), P. 589–592.Kolesnikova S.A., Loonga C.K., de Souzaa N.R., Burnhamb C.J., Moravskyc A.P. Anomalously soft dynamics of water in carbon nanotubes, Physica B, 2006, 385-386, P. 272–274.Kolesnikova S.A., Loonga C.K., de Souzaa N.R., Burnhamb C.J., Moravskyc A.P. Anomalously soft dynamics of water in carbon nanotubes, Physica B, 2006, 385-386, P. 272–274.Popov I., Makeev I. A benchmark solution for 2-D Stokes flow over cavity, Z. Angew. Math.Phys., 2014, 65, P. 339–348.Popov I., Makeev I. A benchmark solution for 2-D Stokes flow over cavity, Z. Angew. Math.Phys., 2014, 65, P. 339–348.Popov A.I., Gerya T., Lobanov I.S., Popov I.Yu. Benchmark solutions for nanoflows. Nanosystems: Phys. Chem. Math., 2014, 5(2), P. 391–399.Popov A.I., Gerya T., Lobanov I.S., Popov I.Yu. Benchmark solutions for nanoflows. Nanosystems: Phys. Chem. Math., 2014, 5(2), P. 391–399.Popov A.I., Gerya T., Lobanov I.S., Popov I.Yu. On the Stokes flow computation algorithm based on Woodbury formula. Nanosystems: Phys. Chem. Math. 2015, 6(1), P. 140–145.Popov A.I., Gerya T., Lobanov I.S., Popov I.Yu. On the Stokes flow computation algorithm based on Woodbury formula. Nanosystems: Phys. Chem. Math. 2015, 6(1), P. 140–145.Gerya T. Introduction to Numerical Geodynamic Modelling. Cambridge: Cambridge University Press, 2010.Gerya T. Introduction to Numerical Geodynamic Modelling. Cambridge: Cambridge University Press, 2010.

The authors declare that there are no conflicts of interest present.